Traps
How JEE Mains Maths costs you marks when you know the maths
A right answer earns 4 and a wrong one loses 1, on multiple-choice and numeric questions alike, on a clock shared with two other subjects. So the first traps below are about the paper, not the mathematics. The rest are the slips that produce the wrong options JEE reuses from shift to shift.
- trap shapes
- 22
- playbooks touched
- 19
- playbooks hit by the widest trap
- 4
- paper-wide, not chapter-specific
- 4
Paper traps — marks lost to the marking and the clock
Nothing to do with any one chapter: the guessing rule for each format, the numeric entry, and the shared clock.
The blank MCQ — expected marks thrown away
Paper-wide — not tied to any one chapter
How it happens
A right answer earns 4 and a wrong one loses 1. A blind guess among four options is worth 1/4 × 4 − 3/4 × 1 = +0.25 on average, and with one option ruled out it is worth 1/3 × 4 − 2/3 × 1 ≈ +0.67.
The check
Before time runs out, answer every MCQ. Rule out what you can on sight — a sign that cannot be right, a value outside the allowed range — and pick from what is left.
The guessed numeric answer — almost always −1
Paper-wide — not tied to any one chapter
How it happens
A numeric answer has no options, so a guess is almost certainly wrong. It carries the same −1 as a wrong MCQ, so its expected value is close to −1.
The check
Enter a numeric answer only when you have worked it out. If you have not, leave it blank; the MCQ rule does not carry over.
A right method, a wrong entry
Paper-wide — not tied to any one chapter
How it happens
The numeric answer is expected as an integer and must be entered exactly. A rounding slip, a unit left unconverted or a factor dropped at the last line scores −1, the same as a wrong method.
The check
If the working ends in a non-integer, treat it as a sign of a slip and recheck the last steps. Reread what the question asks for — the value, its square, a sum of parts — before typing.
The stuck Maths question on a shared clock
Paper-wide — not tied to any one chapter
How it happens
Maths, Physics and Chemistry share one three-hour clock, and every question pays the same 4 marks. Ten minutes on one hard integral can cost several questions you would have answered in a minute each in another subject.
The check
Two passes. On the first, answer what opens up quickly and mark the rest. If a question has not opened up in about three minutes, mark it, move on, and come back only once every subject has had its first pass.
Cornerstone traps — where the most marks go
The slips that cost marks in the chapters the paper leans on hardest. Each wrong answer they produce is printed among the options.
Features that do not move with the centre
Affects: Conic Sections
How it happens
The standard results — focus (a, 0), directrix x = −a, the slope-form tangent — are for a conic at the origin. For (y − k)² = 4a(x − h) the focus is (h + a, k), and a distractor keeps (a, 0).
The check
Complete the square first and read off the centre or vertex. Work in shifted coordinates, then shift every feature back by the same (h, k).
The ellipse result used on a hyperbola
Affects: Conic Sections
How it happens
The two curves share formulas up to one sign: b² = a²(1 − e²) against b² = a²(e² − 1), the tangency condition c² = a²m² + b² against c² = a²m² − b², the director circle radius² a² + b² against a² − b². Options are built from the other curve's sign.
The check
Name the curve before you write any formula. For a hyperbola, every b² term changes sign; check the eccentricity comes out above 1.
Cosine where the line-plane angle needs sine
Affects: 3D Geometry, Vector Algebra
How it happens
The dot product of the line's direction with the plane's normal gives the angle with the normal. The angle with the plane is its complement, so the formula uses sin θ, and the cosine value appears among the options.
The check
Line with line or plane with plane: cosine. Line with plane: sine. Take the absolute value of the dot product for the acute angle.
Reflexive and symmetric is not an equivalence
Affects: Relations and Functions
How it happens
Many relations in these questions are reflexive and symmetric but fail transitivity, such as |a − b| ≤ 1: 1 is related to 2 and 2 to 3, but 1 is not related to 3. The option calling it an equivalence relation is the trap.
The check
Test transitivity with a chain that crosses the limit, not with nearby points. One failing chain settles it.
A domain read off the simplified formula
Affects: Relations and Functions, Inverse Trigonometric Functions, Limits and Continuity
How it happens
The domain of f(g(x)) excludes every x where g is undefined, even when the composite simplifies to a formula defined there. A denominator, a logarithm or an inverse-trig argument outside [−1, 1] leaves gaps that the simplified formula hides.
The check
Write down the domain of the inner function first, then add the condition that its value lies in the outer function's domain. Simplify only after that.
A bound that is never reached
Affects: Sequences and Series, Application of Derivatives, Complex Numbers, Trigonometric Identities
How it happens
AM–GM, the triangle inequality and |sin x| ≤ 1 give bounds, but a bound is the least or greatest value only if equality can happen. If the equal-pieces point is negative or outside the stated range, the true extreme is elsewhere.
The check
After finding a bound, find the point where equality holds and check it is allowed. If it is not, the bound is an option built to catch you.
Core traps — slips in the middle chapters
A dropped case, an extra root, a sign: slips in method rather than hard questions.
The greatest integer of a negative number
Affects: Definite Integration, Limits and Continuity
How it happens
[x] is the next integer to the left, so [−0.3] = −1, not 0. On an interval below zero, taking [x] as the integer part toward zero shifts every piece by one.
The check
Split the interval at every integer and write [x] on each piece before integrating. On negative pieces, check one value such as [−0.5] = −1.
The signed integral given as the area
Affects: Application of Integrals, Definite Integration
How it happens
The integral of sin x from 0 to 2π is 0, but the area is 4. Where a curve crosses the axis, or the upper and lower curves swap, the integral cancels pieces that the area adds.
The check
Find every crossing inside the interval, split there, and add the pieces as positive numbers.
A region with no x ≥ 0
Affects: Application of Integrals
How it happens
Without x ≥ 0, a region such as xy ≤ k, 1 ≤ y ≤ x² includes every x ≤ −1, where xy ≤ 0 ≤ k always holds, so it is unbounded. The printed options assume the first quadrant.
The check
Sketch the region on both sides of the y-axis. If one side runs off to infinity, answer for x ≥ 0, the region the options assume.
Choosing the 'at least one' first
Affects: Permutations and Combinations, Probability
How it happens
Picking one required item first and then filling the rest freely counts the same selection several times, once for each required item it contains. The inflated count sits among the options.
The check
Count the complement: total minus the selections with none. Or split by exactly one, exactly two and so on, and add.
Conjugate roots without real coefficients
Affects: Complex Numbers, Quadratic Equations
How it happens
Non-real roots come in conjugate pairs only when the coefficients are real. With a complex coefficient, one root being 2 + i says nothing about 2 − i.
The check
Check the coefficients before using the conjugate. If they are complex, use the sum and product of the roots instead.
The extra root from squaring
Affects: Complex Numbers, Inverse Trigonometric Functions, Trigonometric Equations
How it happens
Squaring both sides also solves the equation with the opposite sign. Roots of that other equation survive into the answer, and taking tangents of both sides does the same with the range of an angle.
The check
Put every root back into the original equation. A modulus is never negative, and an inverse-trig sum must land in its range.
The x² coefficient that can vanish
Affects: Quadratic Equations, Relations and Functions
How it happens
When the leading coefficient holds a parameter, the value that makes it 0 leaves a linear equation, and the discriminant test does not apply to it. That value is often the one the options include or leave out.
The check
Set the leading coefficient to 0 first and solve that case on its own. Then run the discriminant for the rest.
D > 0 where the question allows D = 0
Affects: Quadratic Equations, Application of Derivatives
How it happens
Real roots means D ≥ 0; distinct real roots means D > 0. 'Increasing for all x' likewise allows f′ to touch 0 at one point, so options that differ only at the boundary value test this.
The check
Read whether the question says real, distinct or equal. Then test the boundary value itself before choosing between a strict and a non-strict answer.
Long-tail traps — ranges, signs and endpoints
Principal ranges, determinant powers, one-sided limits and interval endpoints.
An angle outside the principal range
Affects: Inverse Trigonometric Functions, Complex Numbers, Differentiation
How it happens
sin⁻¹ and tan⁻¹ return angles in [−π/2, π/2] and cos⁻¹ in [0, π], so sin⁻¹(sin 2) is π − 2, not 2. For z = −1 + i, tan⁻¹(y/x) gives −π/4 but arg z is 3π/4.
The check
Before cancelling an inverse with its function, check the angle lies in the principal range; if not, move it there. For arg z, check which quadrant z is in.
|kA| taken as k|A|
Affects: Matrices, Determinants
How it happens
For an n × n matrix, |kA| = kⁿ|A| and |adj A| = |A|ⁿ⁻¹, so for a 3 × 3 matrix |2A| = 8|A|. Dividing by a negative |A| also flips a sign that options are built to catch.
The check
Write the order n next to every determinant step. Carry the sign of |A| through any division.
One side of the limit taken for both
Affects: Limits and Continuity, Differentiation
How it happens
At an integer n, [x] tends to n − 1 from the left and n from the right, and |x|/x tends to −1 and 1 at 0. The limit exists only when both sides agree, and the same holds for the left and right derivatives.
The check
At every integer point of [x], every zero of a modulus and every joint of a piecewise function, work out the left and right values separately.
Solutions and extremes at the endpoints
Affects: Trigonometric Equations, Application of Derivatives
How it happens
On [0, 2π], sin x = 0 has three solutions, 0, π and 2π; on (0, 2π) it has one. A greatest or least value on a closed interval can sit at an endpoint rather than at a turning point.
The check
Read whether the interval is open or closed, then test each endpoint. Also check that no denominator such as tan x vanishes at a solution you counted.
Two habits cover most of this page
Before you solve
Check the options first
Rule out anything out of range or with the wrong sign. It often leaves one option, and when it does not, it makes the end-of-paper guess worth more.
On the paper
Two passes, then fill the MCQs
Answer the quick ones first and mark the rest. At the end, every multiple-choice question gets an answer; a numeric answer you have not worked out stays blank.